A002641 Numbers k such that (k^2 + k + 1)/7 is prime.

4, 9, 11, 23, 32, 39, 44, 51, 53, 60, 65, 72, 86, 93, 95, 114, 123, 156, 170, 179, 186, 200, 207, 212, 219, 228, 233, 240, 249, 261, 270, 303, 317, 333, 338, 345, 375, 389, 401, 443, 452, 473, 480, 492, 515, 534, 548, 564, 578, 585, 597, 599, 611, 641, 660, 662

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 1, pp. 245-259.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929. [Annotated scans of a few pages from Volumes 1 and 2]

Crossrefs

Subsequence of A047348.

Programs

Magma

/* See Crossrefs: */
A047348:=[m: m in [1..700] | m mod 7 in [2,4]];
[n: n in A047348 | IsPrime( (n^2+n+1) div 7 )];
// Bruno Berselli, Sep 26 2012

Mathematica

Select[Range[700], PrimeQ[(#^2 + # + 1)/7] &] (* Harvey P. Dale, Sep 16 2011 *)

PARI

is(n)=isprime((n^2+n+1)/7) \\ Charles R Greathouse IV, May 22 2017

Extensions

More terms from Jon E. Schoenfield, Mar 24 2010